On a One-Dimensional Differential Game with a Non-convex Terminal Payoff

  • Igor’ V. Izmest’evEmail author
  • Viktor I. Ukhobotov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12095)


A one-dimensional differential game is considered, in which the payoff is determined by the modulus of the deviation of the phase variable at a fixed time from the set value, taking into account the periodicity. The first player seeks to minimize the payoff. The goal of the second player is the opposite. For this problem, the price of the game is calculated and optimal player controls are constructed. As an example, we consider the problem of controlling a rotational mechanical system in which the goal of the first player acquires the meaning of minimizing the modulus of deviation of the angle from the desired state.


Control Differential game Payoff 


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Authors and Affiliations

  1. 1.N.N. Krasovskii Institute of Mathematics and MechanicsYekaterinburgRussia
  2. 2.Chelyabinsk State UniversityChelyabinskRussia

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